The Democratic and the Republican Way to Clean the Street
Estimating Partisan Voting in Nonpartisan Offices Using Cast Vote Records
MIT
May 15, 2024
Motivation
Partisanship is embedded in who we are (Campbell et al. 1960; Fiorina 1981; Green, Palmquist, and Schickler 2002) and how political parties represent themselves (Aldrich 2011)
- This extends to the state and local level, both in politics (Hopkins 2018) and policy (Hertel-Fernandez 2019; Grumbach 2022)
Yet, across the U.S., 70% of local governments use nonpartisan election systems where party labels are absent from the ballot (DeSantis and Renner 1991; Svara 2003)
Question
Do patterns in vote choice also fall along a partisan divide in the absence of party labels on the ballot?
Conflicting Expectations
- Progressive reformers around the turn of the 20th century called for changes to insulate government from the pressure of parties and political machines (Bonneau and Hall 2009; Adrian 1952)
Local governments often perform non-ideological work, like paving roads and fixing sewers (Peterson 1981; Oliver, Ha, and Callen 2012; Anzia 2021)
Voter preferences on local issues don’t seem to mirror preferences on national issues (Anzia 2021)
- Voters regularly rely on “heuristics,” especially in low-information elections (Downs 1957; Mondak 1993; Lau and Redlawsk 2001)
- Indeed, research suggests a correlation between local public opinion, elite preferences, and policy outcomes (Tausanovitch and Warshaw 2013; Einstein and Kogan 2016; de Benedictis-Kessner and Warshaw 2016; Einstein and Glick 2018; de Benedictis-Kessner, Jones, and Warshaw 2023; Sievert and McKee 2019; Weinschenk 2022; Kuriwaki 2023)
Data
One of the reasons there are conflicting expectations is that measurement of local preferences is extremely difficult (Anzia 2021)
Survey research is limited by sample size, question wording, survey complexity, and inaccurate reporting
Aggregated data must rely on strong ecological inference assumptions
I take a new approach to this problem, using ballot-level data called cast vote records (CVRs)
- CVRs contain the true votes on all races a voter could have cast a ballot for in the election, but they only contain information on vote choice
- I use CVRs from Adams County, Colorado
Model Estimation
Standard 2-Parameter Item-Response Theory model (Jackman 2009)
Model
\[ \begin{align*} Y_{j, k(c)} &\sim \text{Categorical}(\pi_{j, k(c)}) \\ \pi_{j, k(c)} &= \text{Pr}(y_{jk} = c | \alpha_j, \gamma_{k(c)}, \beta_{k(c)}) = \text{softmax}(\alpha_j \cdot \gamma_{k(c)} - \beta_{k(c)}) \end{align*} \]
| Quantity | Symbol |
|---|---|
| Individual | \(j = 1, 2, …, J\) |
| Race | \(k = 1, 2, …, K\) |
| Candidate | \(c = 1, 2, …, C\) |
| Ideal point of voter \(j\) | \(\alpha\) |
| Discrimination/Slope Parameter | \(\gamma\) |
| Difficulty/Location Parameter | \(\beta\) |
Model Notes
Identification restrictions are essential Rivers (2003)
Normalize \(\alpha\) to mean 0, standard deviation 1
Let \(\gamma\) vacillate and post-process using the algorithm developed by Papastamoulis and Ntzoufras (2022)
I estimate the model under a Bayesian framework using a bespoke Stan model
Validation – Aggregated Points
Distribution of Ideal Points of Voters for Trump and Biden Voters
Validation – Geographical Distribution
Distribution of Ideal Points by State House District in Adams County, Colorado
Validation – DIME Comparison
Different latent dimensions prevent me from directly comparing estimates, instead I can only compare cutpoints
The definition of cutpoints flows from the spatial utility model for a binary choice between \(\zeta_j\) and \(\psi_j\)
\[ \begin{align*} U_i\left(\zeta_j\right) &= -\left\|\xi_i-\zeta_j\right\|^2+\eta_{i j} \\ U_i\left(\psi_j \right) &=- \left\|\xi_i-\psi_j \right\|^2+v_{i j} \end{align*} \]
where \(\xi_i \in \mathbb{R}^d\) is the ideal point of respondent \(i\) and \(\eta_{i j}\) and \(v_{i j}\) are stochastic shocks
The cutpoint is then defined as \(\frac{(\xi_j + \psi_j)}{2}\) , the point at which a respondent would find themselves indifferent between the two candidates
In the categorical model, I compute a series of pairwise comparisons between candidates
Validation – DIME Comparison
Comparison of the Cutpoints from the Categorical 2-Parameter Model and DIME Scores
Results
Results - Nonpartisan Details
Future Work
- Sample more voters from more geographies, which is currently limited by computational cost
- Variational inference via Pathfinder is one option
- Machine learning prediction, akin to Bonica (2018), is another option
- Model extensions
- Some evidence suggests that local elections are not well-described by a single dimension (Bucchianeri 2020)
- Include contests where voters could choose more than one candidate
- Compare method directly with Lewis (2001) and Reece et al. (2024)
- More than just partisanship (Anzia 2021)